Collapsing vortex filaments and the spectrum of quantum turbulence
V.A. Andryushchenko and S.K. Nemirovskii
Institute of Thermophysics, 1 Lavrentyev Ave., Novosibirsk 630090, Russia Novosibirsk State University, Novosibirsk, Russia
Novosibirsk State University, street. Pirogova, 2, Novosibirsk, 630090, Russia
Received Jule 28 2016
With the use of the method of correlation functions and of the method of quantum vortices configurations, the energy spectrum of the three-dimensional velocity field induced by collapsing (immediately before the implementation reconnection) vortex filaments is calculated. Statement of the problem is motivated by the idea of modeling the classical turbulence by set of chaotic quantized vortex filaments. Among the various arguments, supporting the idea of quasi-classical behavior of quantum turbulence, the strongest is the realization of the Kolmogorov spectrum of type E(k) ∝ k–5/3, resulting in a number of numerical operations. Another goal is con-nected with an important and intensively discussed topic on the role of hydrodynamic collapse in the formation of turbulence spectra. As a result of calculations it was demonstrated that the vortex filament at the moment of contact create a velocity field having a singularity. This configuration a of vortex filaments generates spectrum E(k), close to the Kolmogorov law. A possible cause of this fact, as well as the likely reason for deviation are discussed. The results are discussed from the point of view of both the classical and quantum turbulence.
PACS: 67.25.dk Vortices and turbulence; PACS: 47.37.+q Hydrodynamic aspects of superfluidity; quantum fluids; PACS: 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow.